{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><strong>A Journey Into Math For Machine Learning</strong></center>\n",
    "<center><strong>机器学习之数学之旅</strong></center>\n",
    "<center><strong>之 自适应增强$adaboost$$(adaptive \\ boosting)$</strong></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](boosting.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "今天的主题是**集成学习**中的$adaboost$, 或称作$adaptive \\ boosting$, 首先我们来建立一种概念, 什么是$adaptive \\ boosting$:\n",
    "$adaboost$是**集成学习**的一种, 意思是建立多个**弱分类器**, 然后用这些弱分类器的**线性加权组合**来形成一个**强分类器**. 什么是弱分类器呢, 就是只比胡猜稍微好一点的分类器, 训练这些弱分类器是一个迭代的过程, 在这个过程里, 下一个弱分类器总是更加关注上一个弱分类器没有分好的数据样本, 以弥补之前弱分类器的不足, $adaboost$就是类似\"三个臭皮匠顶个诸葛亮\"的算法.    \n",
    "\n",
    "课程预览:   \n",
    "(一). 建立一种直觉——$adaboost$的可视化;   \n",
    "(二). 从零推导$adaboost$;   \n",
    "(三). $adaboost$的特性;   \n",
    "(四). 代码解读.   \n",
    "\n",
    "首先我们先来通过可视化的方法来建立一种直觉."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from demonstration import *\n",
    "import plotly.graph_objs as go\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "# 在jupyter notebook之内画图\n",
    "init_notebook_mode(connected=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们首先造一些数据, 并把它们画出来:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_gaussian_quantiles\n",
    "# 画两个正态分布的群\n",
    "X1, y1 = make_gaussian_quantiles(cov=2.,\n",
    "                                 n_samples=200, n_features=2,\n",
    "                                 n_classes=2, random_state=1)\n",
    "X2, y2 = make_gaussian_quantiles(mean=(3, 3), cov=1.5,\n",
    "                                 n_samples=300, n_features=2,\n",
    "                                 n_classes=2, random_state=1)\n",
    "X=np.concatenate([X1,X2])\n",
    "y=np.concatenate([y1,1-y2])\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdBu)\n",
    "y[np.where(y == 0)] =-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = Adaboost_Demonstration(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "每次运行\\_\\_next\\_\\_函数, 都会新增加一个弱分类器, 并对当前的强分类器的分类边界进行可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
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      ]
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     "metadata": {},
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   ],
   "source": [
    "A.__next__(plot=True, plot_mode=\"3d\")"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(二). 从零推导$adaboost$:   \n",
    "我们首先有一个弱分类器$h(x)$, 它输出的值非$1$即$-1$, $h(x) \\in \\{1, -1\\}$, $adaboost$的思路是把这些弱分类器的预测结果都加起来, 然后取他们的均值, 在我们的推导过程中, 假设我们要解决的问题是一个二项分类问题, 则我们要把这些弱分类器都加起来取$sign$, 则有:\n",
    "$$H(x)=sign(\\sum_{t=1}^T h^t(x))$$\n",
    "上式中$H(x)$是一个强分类器, $x$是数据或特征值, $t$指的是弱分类器的个数, 上式的意思是对弱分类器的输出值求和并取$sign$, $H(x) \\in \\{1, -1\\}$   \n",
    "\n",
    "然后我们发现只对弱分类器求和好像少了点什么, 没错, 我们要赋予每个弱分类器不同的权重:\n",
    "$$H(x)=sign(\\sum_{t=1}^T \\alpha^t h^t(x))$$\n",
    "上式中$\\alpha$指的是第$t$个弱分类器的权重.   \n",
    "在$adaboost$中, 这么多弱分类器, 是凭什么依据划分的呢, 其实每个弱分类器关注的是前面弱分类器没有分对的数据样本, 比如说第$t$个弱分类器犯了一些错误, 导致有些数据样本没有分对, 那么第$t+1$个弱分类器就会更加关注前面没有分对的数据点, 尝试弥补第$t$个弱分类器的不足."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "假设我们有一些数据样本$\\{(x_{1},y_{1}),\\ldots ,(x_{N},y_{N})\\}$, 其中$y_{i}\\in \\{-1,1\\}$, $N$是数据样本的个数, 我们要解决的是二项分类问题.   \n",
    "我们需要给每一个数据样本赋一个权重, 以控制每个弱分类器应该更加关注哪些数据样本, 我们需要让下一个弱分类器更加关注它前面的弱分类器没有分对的数据点, 设$x_i$在第$t$个弱分类器上的权重为$w^t_i$, 我们首先初始化, 在第$1$个弱分类器上所有数据点的权重都是一样的, 即:\n",
    "$$w^{t=1}_i=\\frac{1}{N}$$\n",
    "初始化错误率$\\epsilon$为, 比如说$100$个数据点, 分错了40个, 则$\\epsilon=0.4$, $\\epsilon$取值在$0$到$1$之间:\n",
    "$$\\epsilon=\\sum_{y_i \\neq h_i(x)}\\frac{1}{N} \\quad \\epsilon \\in [0, 1]$$\n",
    "将$w_i$代入$\\epsilon$, 得出:\n",
    "$$\\epsilon=\\sum_{y_i \\neq h_i(x)}w_i ; \\quad \\sum w_i =1\\tag{eq. 1}$$\n",
    "那我们怎么确定下一个弱分类器需要关注哪些数据样本呢? 当我们定义好当前的弱分类器$h^t(x)$之后, 做以下操作:\n",
    "$$w^{t+1}_{i}=\\frac{w^{t}_{i}}{Z}e^{-\\alpha^t h^t(x_i) y_i}$$\n",
    "上式中$Z$是归一化因子, 因为我们想要$\\sum w_i =1$, 怎么理解这个式子呢, 首先$\\alpha$是正数, 当$h^t(x_i)=y_i$的时候, $h^t(x_i)y_i$的是$1$, 否则是$-1$, 不难看出当当前弱分类器$h^t(x_i)$预测正确的时候, $w^{t+1}=$会变小, 而错误的时候, $w^{t+1}$会变大:\n",
    "$${\\displaystyle w^{t+1}_{i}={\\begin{cases} \\frac{1}{Z} w_{i}^{t}e^{-\\alpha ^{t}}&{\\text{if }}y_{i}=h^{t}(x_{i}),\n",
    "\\\\ \\frac{1}{Z} w_{i}^{t}e^{\\alpha ^{t}}&{\\text{if }}{y_{i} \\neq h^{t}(x_{i})}.\\end{cases}}}\\tag{eq. 2}$$\n",
    "注意我们暂且不管$Z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们现在要求所有未归一的权重的和, 并求出可以使它最小的$\\alpha$, 我们把未归一的权重的和定义为$E$, 因为分错的样本输入到下一个弱分类器的权重(未归一)为$w_{i}^{t}e^{\\alpha ^{t}}$(见$eq.2$), 则分错的样本越多$E$会越大, 相反分对的样本越多$E$越小.\n",
    "$$E=\n",
    "\\sum _{y_{i}=h^{t}(x_{i})}w_{i}^{t}e^{-\\alpha ^{t}}+\\sum _{y_{i}\\neq h^{t}(x_{i})}w_{i}^{t}e^{\\alpha ^{t}}$$\n",
    "上式左边加上$\\sum _{y_{i}\\neq h^{t}(x_{i})} w_{i}^{t} e^{-\\alpha ^{t}}$, 右边再减去.\n",
    "$$E=\n",
    "\\sum _{i=1}^{N}w_{i}^{t} e^{-\\alpha ^{t}}+\\sum _{y_{i}\\neq h^{t}(x_{i})}w_{i}^{t}(e^{\\alpha ^{t}} - e^{-\\alpha ^{t}})$$\n",
    "上式中可看出, 上式左边跟我们当前的弱分类器$h^{t}(x)$无关, 当前的弱分类器只对右式起作用, 也就是右式控制着$E$的大小, 为了得到我们想要的$\\alpha$, 我们要求$E$对于$\\alpha^{t}$的导数, 并把它设为$0$, 求出$\\alpha^{t}$的值, 注意下边我们会把等式左边省略掉, 因为它可看作一个常数."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$${\\frac {d E}{d\\alpha ^{t}}}=-\\sum _{y_{i}= h^{t}(x_{i})}w_{i}^{t}e^{-\\alpha ^{t}}+\\sum _{y_{i}\\neq h^{t}(x_{i})}w_{i}^{t}e^{\\alpha ^{t}}=0$$\n",
    "解上面的式子, 这里省略过程, 因为比较简单, 大概解法是将$e^{\\alpha ^{t}}$和$e^{-\\alpha ^{t}}$提到求和符号外面来, 同时取$\\log$, 化简, 得到$\\alpha^{t}$:\n",
    "$$\\alpha ^{t}={\\dfrac {1}{2}}\\log \\left({\\dfrac {\\sum _{y_{i}=h^{t}(x_{i})}w_{i}^{t}}{\\sum _{y_{i}\\neq h^{t}(x_{i})}w_{i}^t}}\\right)={\\dfrac {1}{2}}\\log  \\left(\\dfrac {1-\\epsilon^{t}}{\\epsilon^{t}}\\right)  $$\n",
    "将$\\alpha ^{t}$带入到$(eq. 2)$里, 得到下式, 注意这里用到了$e^{log_e(x)}=x$:\n",
    "$${\\displaystyle w^{t+1}_{i}=\\frac{1}{Z} w_{i}^{t}{\\begin{cases}  \\sqrt{\\frac{\\epsilon^{t}}{1-\\epsilon^{t}}} &{\\text{if }}y_{i}=h^{t}(x_{i}),\n",
    "\\\\ \\sqrt{\\frac{1-\\epsilon^{t}}{\\epsilon^{t}}} &{\\text{if }}{y_{i} \\neq h^{t}(x_{i})}.\\end{cases}}}\\tag{eq. 3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们求$Z$, $Z$是所有数据样本权重的和也就是所有$w^{t+1}_{i}$取值的和:\n",
    "$$Z=\\sqrt{\\frac{\\epsilon^{t}}{1-\\epsilon^{t}}} \\sum _{y_{i}= h^{t}(x_{i})}w^{t}_i +\n",
    "\\sqrt{\\frac{1-\\epsilon^{t}}{\\epsilon^{t}}} \\sum _{y_{i}\\neq h^{t}(x_{i})}w^{t}_i$$\n",
    "将$\\epsilon=\\sum_{y_i \\neq h_i(x)}w_i$代入上式, 得出:\n",
    "$$Z=\\sqrt{\\frac{\\epsilon^{t}}{1-\\epsilon^{t}}} (1-\\epsilon^t) +\n",
    "\\sqrt{\\frac{1-\\epsilon^{t}}{\\epsilon^{t}}} \\epsilon^t=2 \\sqrt{\\epsilon^t(1-\\epsilon^t)}$$\n",
    "将$Z$代入$(eq.3)$里:\n",
    "$${\\displaystyle w^{t+1}_{i}={\\begin{cases}  \\frac{w_{i}^{t}}{2(1-\\epsilon^{t})} &{\\text{if }}y_{i}=h^{t}(x_{i}),\n",
    "\\\\ \\frac{w_{i}^{t}}{2\\epsilon^{t}} &{\\text{if }}{y_{i} \\neq h^{t}(x_{i})}.\\end{cases}}}\\tag{eq. 4}$$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们通过上式还是很难看出$w^{t+1}_i$的意义到底是什么, 没关系, 接下来就恍然大悟了, 下面我们求数据点中分类正确的样本和分类错误样本各自$w^{t+1}_i$的合:\n",
    "$$\\sum_{y_{i}=h^{t}(x_{i})}w^{t+1}_i=\\frac{\\sum_{y_{i}=h^{t}(x_{i})} w_{i}^{t}}{2(1-\\epsilon^{t})}$$\n",
    "我们又知道$\\sum_{y_{i}\\neq h^{t}(x_{i})} w_{i}^{t}=\\epsilon^t$, 得出$\\sum_{y_{i}=h^{t}(x_{i})} w_{i}^{t}=1-\\epsilon^t$, 代入上式:\n",
    "$$\\sum_{y_{i}=h^{t}(x_{i})}w^{t+1}_i=\\frac{1-\\epsilon^t}{2(1-\\epsilon^{t})}=\\frac{1}{2}$$\n",
    "又因为$\\sum w_i =1$, 得出:\n",
    "$$\\sum_{y_{i} \\neq h^{t}(x_{i})}w^{t+1}_i=1-\\sum_{y_{i}=h^{t}(x_{i})}w^{t+1}_i=1-\\frac{1}{2}=\\frac{1}{2}$$\n",
    "上式的意义是, 在我们每次增加一个新弱分类器的时候, 前面的弱分类器分错的样本的权重占总样本权重的$\\frac{1}{2}$, 前面的弱分类器分对的样本的权重也占总样本权重的$\\frac{1}{2}$"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们把$adaboost$的计算步骤梳理一下:\n",
    "1. 初始化$w^1_i=\\frac{1}{N}$;\n",
    "2. 在第$t$步, 选择可以最小化当前错误率$\\epsilon$的弱分类器, 并添加这个弱分类器, 以降低错误率(如果还没有弱分类器, 那就创建一个), 并计算$\\alpha^t$, $\\alpha ^{t}={\\dfrac {1}{2}}\\log  \\left(\\dfrac {1-\\epsilon^{t}}{\\epsilon^{t}}\\right)$, 定义新的弱分类器为$f^t(x)=\\alpha^t h^t(x))$\n",
    "3. 计算新的数据样本权重$w^{t+1}_i$, 见$(eq. 4)$\n",
    "4. 回到第2, 直到收敛.\n",
    "5. 得到的模型为: $H(x)=sign(\\sum_{t=1}^T \\alpha^t h^t(x))$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(三). $adaboost$的特性:\n",
    "1. 易用, 需要调节的参数少;\n",
    "2. 弱分类器可以是任何模型, 比如逻辑回归, 线性回归等等, 最常用的是决策树桩;\n",
    "3. 对数据敏感, 如果数据有很多噪音, 则$adaboost$会倾向于拟合噪音而最终导致模型的过拟合, 为了解决这样的问题, 可以给每一个弱分类器一个学习率权重, 让每个弱分类器最强分类器造成的影响小一些, 或做交叉验证, 让迭代的过程在合适的时机停止;\n",
    "4. 可以用来做特征选择, 举个例子吧， 比如说要评估人群的信用风险, 然后你会有很多这些人的资料, 比如说性别年龄, 居住地址, 收入, 有无不动产等等, 如果你用$adaboost$的集成方法来做分类, 在迭代的每一步你需要用一个弱分类器划分数据样本, 假设我们用决策树桩， 决策树桩每次只能选择一个特征值进行划分, 在建模完成之后, 看一下模型里的弱分类器都是靠那些特征进行分类的, 就可以得出每种特征的重要性, 方便我们做特征选择, 剔除多余的特征, 增加计算效率， 减少噪音;\n",
    "5. 注意, 在推导的过程中, 我们对强分类器输出的结果取$sign$, 实际中我们可以不单纯取$sign$, 而是找一个分类最好的阈值, 或者说边界, 这个阈值不一定为$0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(四). 代码解读.   \n",
    "请参照B站或youtube视频讲解, 或参考demonstration.py文件内注释.   "
   ]
  },
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   "source": []
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